The Times of your Life
Contents
The basic unit of time is the second.
The second is defined as the duration of 9,192,631,770 periods of the radiation
corresponding to the transition between two hyperfine levels of the ground
state of cesium 133. The UT
times (based on the terrestrial rotation), with a
day of length 86400 seconds (by definition), are kept in line with the
occasional addition of leap seconds.
Times based on the Sun include :
- Local Solar time This is what God gave us. The Sun transits (crosses
the meridian) at noon, local time. This works just fine for farmers, but
there are two difficulties for civilized man with quartz timepieces. The
length of the Solar day (noon to noon) varies during the year
due to the eccentricity of the terrestrial orbit. In
addition, when your sundial reads noon, your neighbor's doesn't (unless
it lies directly north or south of yours). Local time is a local
phenomenon.
- Civil Time This is what the railroads standardized in the
19th
century, to overcome the problems associated with local time (Whose local
time do you set your watch to?). Since the
day is 24 hours long, the angular velocity of the Sun is
15o per hour.
Civil time consists of 24 time zones, each 15o wide, centered
on lines
of longitude which are multiples of 15o
(there are local variations).
The Eastern time zone is
centered on 75o west longitude.
Noon EST occurs when the fictitious
mean Sun crosses the 75th degree of longitude.
The fictitious mean
Sun differs from the true Sun in that it has a constant angular velocity
across the sky. The difference (in time) between the true Sun and the
fictitious mean Sun, the Equation of Time, reaches nearly +/-15 minutes.
The analemma on older globes demonstrates the Equation of Time.
Standard time and daylight time are all parts of Civil time.
- Universal Time is the zero-point of civil time.
UT is the civil time
at 0o longitude (the standard meridian), which
passes through Greenwich,
England. UT is also known as Greenwich mean time (GMT), and is military
time Zulu (Z). UT is based on the fictitious mean Sun.
UT = 12h + the Greenwhich hour angle (GHA) of the
fictitious mean Sun.
UT1 is UT corrected for the motion of the geographic poles (the Chandler
wobble and similar phenomena).
UT2 is UT1 with an extrapolated correction for the spindown
of the Earth.
UTC (Coordinated Universal time) is basically UT1, rounded off. Leap
seconds are added to keep UTC within 0.9 sec of UT1. UTC is broadcast by
WWV radio. You can see this time on the seismograph in the ESS lobby.
- Atomic Time TAI is kept by atomic clocks.
It is very accurate, and is not
affected by the vagaries of solar system dynamics.
0:00:00 TAI = 0:00:00 UT2 1/1/1958.
- Ephemeris Time ET, like UT, is based on the mean fictitious Sun, but
one with the angular velocity of the Sun on 1900 0.5 January. The right
ascension of the fictitious mean Sun is given by the expression
RA=18h38m45.836s +
8,640,184.542s TE + 0.0929s
TE2
where TE is the number of Julian centuries (36525 days)
since 1900 0.5 January.
ET-UT = 24.349s + 72.318sTE
+ 29.950sTE2
Ephemeris time was formally abolished in 1984, and was replaced with
Terrestrial Dynamical Time (TDT) and Terrestrial Barycentric Time (TBT).
Astronomers realized a long time ago that the civil time system is cumbersome
for determining lengths of intervals. Just how many days have passed since
July 4, 1776? To get around some of these dificulties, astronomers generally
use Julian dates. The Julian date is the number of
ephemeris days elapsed since 12h UT on 1 January, 4713 BC (which is
-4712 AD). The Julian date on January 1.5, 2000 will be 2,451,545.0. This is
defined as J2000.0. Note that the JD increments at 12h UT (Greenwich
Mean Time).
Because the JD is a large number, you will often see the
Reduced Julian Date (JD-2,400,000) used. The
modified Julian Date (MJD) is also commonly used. MJD=JD-2,400,000.5.
Note the extra 0.5 day in the definition. Modified Julian dates increment at the
same time as Universal Time. Some have been known to use HJD=JD-0.5.
Be sure you know what convention is being used.
Times in the Batten catalog are in Reduced Julian Days.
To convert the civil time into the Julian day, use the following
algorithm
JD = fix(365.25*f) + fix(30.6001*(g+1)) + d + A + 1,720,994.5
where y is the year, m is the month, d is the day of the month,
f=y for m>2 and f=y-1 for m<3
g=m for m>2 and g=m+12 for m<3
A=2-fix(f/100) + fix(f/400).
This algorithm works for Gregorian civil calendar dates only.
When you compute with Julian dates, be sure to use double precision
floating point arithmetic.
The IDL procedure JULDATE will return the reduced Julian date. In IDL,
type juldate,jd, and you will be prompted for input.
Sidereal Time
is based on the Earth's sidereal
rotation period (rotation with respect to the stars). The length of
the sidereal day is 24 sidereal hours, or
23h56m4s Solar time. The difference is due
to the angular motion of
the earth around the Sun. In a year there is one more sidereal day than Solar
day. The sidereal time is a measured locally. The local sideral time (LST) is
the right ascension of the zenith. The hour angle HA of an object with right
ascension RA is given by HA=LST-RA
Right ascension is generally measured in units of time, not
degrees of arc.
24 hours of time corresponds to 360 degrees of arc at the equator.
Therefore,
- 1h=15o/cos(
)
- 1m=15'/cos(), and
- 1s=15"/cos()
where is
the declination of the target. You can use analogous formulae
to convert degrees of arc to distances on the earth's surface.
The basic reference for all this is the Astronomical Almanac,
available in the reference section of the library. It is published annually.
Some Web sites: